The game started brightly and there were chances at either end in the opening minutes. City striker Jamie Mackie burst into the box in the second minute and saw his close range effort smothered by goalkeeper Nikki Bull.
John Gayle then went close for the Shots when he rifled a shot a yard wide from the edge of the box.
The game continued to flow well and Aldershot should have taken the lead. Ryan Williams curled in a corner and Marcus Gayle's bullet header was superbly tipped over the bar by City goalkeeper Martin Rice when it appeared to be heading for the top corner.
The Shots pressed again late in the first half as Ryan Scott headed narrowly wide from another Williams cross and Louis Soares had a shot charged down bravely by Dean Moxey.
After the break Exeter started well and defender Billy Jones twice went close to scoring in the opening minutes.
He curled a free-kick at the foot of the post and forced Bull to tip the ball past the post. Then the defender tried his luck from 20 yards and struck the ball just over the bar from a tight angle.
Aldershot were always dangerous. Soares controlled the ball and picked his spot but the ball flew narrowly over the bar.
At the other end Mackie then burst into the box and had a big shout for a penalty turned down after he appeared to be tripped.
Exeter then brought on Adam Stansfield as they desperately searched for a winner. The striker appeared to be through on goal when he collected a long ball but was denied when Bull rushed off his line to charge the ball down.
At the other end substitute Joel Grant went close for the Shots in the dying minutes. He controlled the ball and thumped a great strike from 25 yards which was superbly tipped over by Rice.
Exeter almost grabbed a winner in injury time. Jones' cross was met by substitute by Jon Challinor and he headed the cross agonisingly just past the post.